diff -r f72cc96a58c6 -r 06c510d40ebb src/SbpOperators/readoperator.jl
--- a/src/SbpOperators/readoperator.jl	Tue Feb 08 10:58:31 2022 +0100
+++ b/src/SbpOperators/readoperator.jl	Thu Feb 10 09:58:36 2022 +0100
@@ -4,6 +4,7 @@
 export get_stencil_set
 
 export parse_stencil
+export parse_nested_stencil
 export parse_scalar
 export parse_tuple
 
@@ -106,6 +107,25 @@
     end
 end
 
+
+"""
+    parse_nested_stencil(parsed_toml)
+
+
+"""
+function parse_nested_stencil(parsed_toml)
+    if parsed_toml isa Array
+        weights = parse_stencil.(parsed_toml)
+        return CenteredNestedStencil(weights...)
+    end
+
+    center = parsed_toml["c"]
+    weights = parse_tuple.(parsed_toml["s"])
+    return NestedStencil(weights...; center)
+end
+
+
+
 """
     parse_scalar(parsed_toml)
 

diff -r f72cc96a58c6 -r 06c510d40ebb test/SbpOperators/readoperator_test.jl
--- a/test/SbpOperators/readoperator_test.jl	Tue Feb 08 10:58:31 2022 +0100
+++ b/test/SbpOperators/readoperator_test.jl	Thu Feb 10 09:58:36 2022 +0100
@@ -4,6 +4,7 @@
 using Sbplib.SbpOperators
 
 import Sbplib.SbpOperators.Stencil
+import Sbplib.SbpOperators.NestedStencil
 
 @testset "readoperator" begin
     toml_str = """
@@ -170,3 +171,15 @@
     @test SbpOperators.parse_rational(2) isa Rational
     @test SbpOperators.parse_rational(2) == 2//1
 end
+
+@testset "parse_nested_stencil" begin
+    toml = TOML.parse("""
+        s1 = [["1/2", "1/2", "0"],[ "-1/2", "-1", "-1/2"],["0", "1/2", "1/2"]]
+        s2 = {s = [[  "2",  "-1", "0"],[   "-3",  "1",    "0"],["1",   "0",   "0"]], c = 1}
+        s3 = {s = [[  "2",  "-1", "0"],[   "-3",  "1",    "0"],["1",   "0",   "0"]], c = 2}
+    """)
+
+    @test parse_nested_stencil(toml["s1"]) == CenteredNestedStencil((1//2, 1//2, 0//1),( -1//2, -1//1, -1//2),(0//1, 1//2, 1//2))
+    @test parse_nested_stencil(toml["s2"]) == NestedStencil((2//1, -1//1, 0//1),( -3//1, 1//1, 0//1),(1//1, 0//1, 0//1), center = 1)
+    @test parse_nested_stencil(toml["s3"]) == NestedStencil((2//1, -1//1, 0//1),( -3//1, 1//1, 0//1),(1//1, 0//1, 0//1), center = 2)
+end